Algebra worksheet — GCSE Foundation

1.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

2.Solve 2x² − 32 = 0.

3.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

4.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

5.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

6.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

7.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

8.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

9.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

10.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

11.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

12.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

13.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

14.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

15.Write down the gradient of the line with equation y = 6 + 4x.